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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The double bubble problem on the flat two-torus


Authors: Joseph Corneli, Paul Holt, George Lee, Nicholas Leger, Eric Schoenfeld and Benjamin Steinhurst
Journal: Trans. Amer. Math. Soc. 356 (2004), 3769-3820
MSC (2000): Primary 53A10; Secondary 49Q10
Published electronically: March 12, 2004
MathSciNet review: 2055754
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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the perimeter-minimizing double bubbles on all flat two-tori and, as corollaries, on the flat infinite cylinder and the flat infinite strip with free boundary. Specifically, we show that there are five distinct types of minimizers on flat two-tori, depending on the areas to be enclosed.


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Additional Information

Joseph Corneli
Affiliation: C/O Frank Morgan, Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267 – and – Department of Mathematics, University of Texas, Austin, Texas 78712
Email: Frank.Morgan@williams.edu, jcorneli@math.utexas.edu

Paul Holt
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: pholt@wso.williams.edu

George Lee
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: lee43@fas.harvard.edu

Nicholas Leger
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: nickleger@mail.utexas.edu

Eric Schoenfeld
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: eschoenf@wso.williams.edu

Benjamin Steinhurst
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: Benjamin.A.Steinhurst@williams.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03551-2
PII: S 0002-9947(04)03551-2
Received by editor(s): June 16, 2003
Published electronically: March 12, 2004
Article copyright: © Copyright 2004 American Mathematical Society